Due to the changes which may occur in their parameters, systems are usually demonstrated by some subsystems for different conditions. This paper employs Modified Petri Nets (MPN) to model theses subsystems and makes it simple to analyze them. In this method, first, the continuous transfer function is converted to a discrete transfer function and then, by MPN, system is modeled and analyzed. All...

This article considers the relation between spanning properties of lattice orbits discrete series representations and associated co-volume. The focus is on density theorem, which provides a trichotomy characterizing existence cyclic vectors separating vectors, frames Riesz sequences. We provide an elementary exposition that based solely basic tools from harmonic analysis, representation theory,...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

We consider Schrödinger operators with periodic potentials on discrete graphs. Their spectrum consists of a finite number bands. determine trace formulas for the operators. The proof is based decomposition into direct integral and specific representation fiber traces are expressed as Fourier series quasimomentum. coefficients given in terms cycles quotient graph from some cycle sets. also prese...